Computing singularities of the spectra of representation rings of finite groups

André Gimenez Bueno; Renato Vidal Martins; Edney Oliveira; Csaba Schneider

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arXiv · 1910.08767

Computing singularities of the spectra of representation rings of finite groups

André Gimenez Bueno·Renato Vidal Martins·Edney Oliveira·Csaba Schneider

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Abstract

Let $G$ be a finite group of order $n$, and $\xi$ an $n$-th primitive root of unity. Consider the affine scheme $C:=\mbox{Spc}({\mathbb Z}[\xi]\otimes_{\mathbb Z} R(G))$ where $R(G)$ is the representation ring of $G$. We study the fibers of the formal tangent sheaf of $C$ by computing their dimension and also finding (and measuring) the singularities of $C$. We present explicit computations for noncommutative groups of small order, and develop practical methods to compute these invariants for an arbitrary finite group.

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BibTeX RIS

André Gimenez Bueno, Renato Vidal Martins, Edney Oliveira, Csaba Schneider. 2019-10-19. Computing singularities of the spectra of representation rings of finite groups. https://arxiv.org/abs/1910.08767

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